Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2021 / Paper 1 / 8 / c / Solution

Because $a_0\ne 0$, the lowest-power equation from part (b) requires the indicial equationThe two candidate indicial roots are thereforeTheir difference is the integer one, so the smaller-root coefficient equation at $k=1$ needs examination rather than automatic division.